Question

In the given figure, AC=CE and AB||ED. Find the value of $x$.

• A. 15 units
• B. 10 units
• C. 25 units
• D. 35 units

Answer 1

The correct option is A 15 units

$\text{In}\Delta ABC\text{and}\Delta EDC,AC=CE\text{(Given)}\angle BAC=\angle DEC\text{(Since AB||DE and AE is a transversal, so they are alternate angles)}\angle ACB=\angle ECD\text{(Vertically opposite angles)}\therefore \Delta ABC\cong \Delta EDC\text{(ASA congruence criteria)}\therefore AB=DE\text{(Sides of congruent triangles)}\therefore x+10=2x-5\Rightarrow x=15units$